A Stochastic Optimization approach for the design of Individualized Dosage Regimens

Abstract

Quantitative methods for individualizing and optimizing the dosage regimen and clinically monitoring each patient are desirable to insure that each patient can obtain effective therapeutic benefit while minimizing undesirable side effects. This is of special concern for medicines that are expensive or whose toxic side effects are severe (e.g., oncological agents). The optimal dosage regimen for an individual is a combination of dose amount and/or dosing interval (i.e., time between doses) which minimizes the risk that the drug exposure deviates from the desired therapeutic window. The therapeutic window is defined as the range of drug exposure (e.g., blood concentration, area under the curve concentration‐time) which is below a threshold defining an acceptable toxic side effect and above a threshold defining a minimum acceptable level of therapeutic efficacy. In this work, the dosage regimen optimization problem defined in terms of general pharmacometric models (i.e., described by differential‐algebraic equations) is presented and a solution approach outlined which uses a scenario‐based stochastic optimization formulation that minimizes a risk metric. The scenarios are derived from the posterior joint probability distribution of the individual's pharmacometric parameters which is obtained following an approximate Bayesian inference approach. A Smolyak rule is used for the selection of the scenarios (i.e., combination of pharmacometric parameters) to be considered and for computing the approximation to the risk metric. Two case studies, gabapentin and cyclophosphamide, are presented to elucidate the advantages and limitations of the proposed approach. The numerical results demonstrate that low risk optimal solutions can be generated via the proposed stochastic optimization; while significantly reducing the computational burden in comparison with the conventional Markov chain Monte Carlo—grid search approach. This partially alleviates implementation issues preventing the deployment of dosage regimen individualization in clinical practice. Since stochastic optimization has been extensively used in other domains, the approach for uncertainty characterization proposed in this work may have general relevance beyond the pharmacometrics domain. © 2013 American Institute of Chemical Engineers AIChE J, 59: 3296–3307, 2013

Model-Based Individualized Treatment of Chemotherapeutics: Bayesian Population Modeling and Dose Optimization

“…Moreover, the dosing strategy employed can depend on the degree to which the patient response can change over time. In some cases, the optimal dosing once determined can be repeated for a number of dosing cycles, unchanged [ 40 ]. In other situations, model mismatch and changes in patient response over time require repeated dose adjustments as patient response is tracked.…”

Advances in Integrated and Sustainable Supply Chain Planning

“…More recently, Laínez-Aguirre and Reklaitis (2013) have proposed a strategy to characterize the probability distribution of uncertain parameters and more appropriately select the scenarios to include into a stochastic program. The authors propose to employ a Bayesian framework to infer the probability distributions from the data collected during observation (e.g., historical demand).…”

“…It is noteworthy that sampling techniques can be used to approximate the continuous probability functions included in the stochastic program to discrete functions. Another appropriate technique can be the utilization of quadrature rules (Laínez-Aguirre and Reklaitis 2013). By doing so, an approximate deterministic equivalent program can be obtained for most stochastic programs.…”